2011/10/14 by Makito Oi, Takahiro Mizusaki, T. Mizusaki
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Ansatz #Atomic and Molecular Physics #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Complex conjugate #Excited state #Fermion #Fock space #Fock state #Hartree–Fock method #Mathematical analysis #Mathematical physics #Mathematics #Norm (philosophy) #Parity (physics) #Pfaffian #Physics #Quantum mechanics #nucl-th
paper · pdf · doi:10.1016/j.physletb.2011.12.040
published as Phys. Lett. B 707, 305-310 (2012) · 14 pages (12pts), no figure
arxiv created 2011/10/14 · openalex publication_date 2011/12/21 · arxiv updated 2012/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A formula to calculate the norm overlap between Hartree–Fock–Bogoliubov (HFB) states with odd number parity (one quasi-particle excited states) is derived with the help of Grassmann numbers and Fermion coherent states. The final formula is expressed in terms of a product of the Pfaffian for a neighboring even–even system (the zero quasi-particle state), and an extra factor consisting of the Bogoliubov transformation matrix and the anti-symmetric matrix in Thoulessʼ HFB ansatz for the even–even system.